Question
Pipes A and B alone can fill a tank in 3 hours and 5
hours respectively. When both pipes along with pipe C, an outlet pipe, are opened together, 2/3 of the tank gets filled in 90 minutes. Find the time taken by pipe C to empty a completely filled tank.Solution
Let the total capacity of the tank be 15 litres. Efficiency of Pipe 'A' = 15 / 3 = 5 litres/hour. Efficiency of Pipe 'B' = 15 / 5 = 3 litres/hour. Let pipe 'C' empties the tank with an efficiency of 'c' litres/hour. Tank filled in 90 minutes = (2/3) × 15 = 10 litres. ATQ, (5 + 3 - c) × (90/60) = 10. (8 - c) × 1.5 = 10. 12 - 1.5c = 10. 1.5c = 2. c = 4/3 litres/hour. Time taken by C to empty the tank = 15 / (4/3) = 15 × (3/4) = 11.25 hours.
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